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Mirrors > Home > ILE Home > Th. List > ssun1 | Unicode version |
Description: Subclass relationship for union of classes. Theorem 25 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ssun1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 632 |
. . 3
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2 | elun 3078 |
. . 3
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3 | 1, 2 | sylibr 137 |
. 2
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4 | 3 | ssriv 2943 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 |
This theorem is referenced by: ssun2 3101 ssun3 3102 elun1 3104 inabs 3162 reuun1 3213 un00 3257 undifabs 3294 undifss 3297 snsspr1 3503 snsstp1 3505 snsstp2 3506 prsstp12 3508 sssucid 4118 unexb 4143 dmexg 4539 fvun1 5182 dftpos2 5817 tpostpos2 5821 ressxr 6866 nnssnn0 7960 un0addcl 7991 un0mulcl 7992 bdunexb 9375 |
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